This equation becomes identical to the equation of motion in the soft-wall AdS/QCD if \(\zeta _\perp \)  is identified with the fifth dimension \(z\)  in AdS space and the wave function \(\phi (\zeta )\)  is identified with the string modes \(\Phi (z)\) . This holographic mapping can be exactly verified using the matrix elements of the current operator and the energy-momentum tensor [1]}, [2]}.
Thus the confining interaction is uniquely determined by the holographic boundary condition as \(V_\perp (\zeta _\perp ) = \kappa ^4 \zeta _\perp ^2 + 2\kappa (J-1)\) , where \(J\)  is the total angular momentum. \(\kappa \)  is the strength of the holographic confinement. From Eq. (REF ), the mass eigenvalues \(M^2_{\perp } = 2\kappa ^2 (2n+|m|+J)\) , follow the Regge trajectories \(M^2 \propto n,L,J\) , where \(n,m\)  are the radial and angular quantum numbers in the transverse plane (\(\vec{\zeta }_\perp \) ). \(L\)  is the orbital angular momentum (\(m\)  is its magnetic projection). The obtained wave functions \(\phi _{nm}\)  are 2D harmonic oscillator functions of the holographic variable \(\zeta _\perp \)  or its conjugate moment \(k_\perp /\sqrt{x(1-x)}\) . In particular, LFH predicts a massless pion (\(n=m=J=0\) ) in the chiral limit, with the light-front wave function \(\psi _\pi (x, \vec{k}_\perp ) = (4\pi /\kappa )\exp \big [-\vec{k}_\perp ^2/(2\kappa ^2x(1-x))\big ]\) .
